%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP064^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n028.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 04:01:51 EDT 2023

% Result   : Theorem 20.57s 20.79s
% Output   : Proof 20.57s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_nat,type,
    nat: $tType ).

thf(ty_real,type,
    real: $tType ).

thf(ty_genClo1015804716orrect,type,
    genClo1015804716orrect: nat > real > $o ).

thf(ty_p,type,
    p: nat ).

thf(ty_ord_max_real,type,
    ord_max_real: real > real > real ).

thf(ty_one_one_nat,type,
    one_one_nat: nat ).

thf(ty_m,type,
    m: nat ).

thf(ty_plus_plus_nat,type,
    plus_plus_nat: nat > nat > nat ).

thf(ty_genClo1163638703lle_te,type,
    genClo1163638703lle_te: nat > nat > real ).

thf(ty_ord_less_eq_real,type,
    ord_less_eq_real: real > real > $o ).

thf(ty_l,type,
    l: nat ).

thf(ty_i,type,
    i: nat ).

thf(sP1,plain,
    ( sP1
  <=> ( genClo1015804716orrect @ m @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ~ ( ( ord_less_eq_real @ ( ord_max_real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) )
         => ~ sP1 )
     => ( genClo1015804716orrect @ m @ ( ord_max_real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: real,X2: real] :
        ( ~ ( ( ord_less_eq_real @ X1 @ X2 )
           => ~ ( genClo1015804716orrect @ m @ X2 ) )
       => ( genClo1015804716orrect @ m @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: nat,X2: real,X3: real] :
        ( ~ ( ( ord_less_eq_real @ X2 @ X3 )
           => ~ ( genClo1015804716orrect @ X1 @ X3 ) )
       => ( genClo1015804716orrect @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( ord_less_eq_real @ ( ord_max_real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) )
     => ~ sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( genClo1015804716orrect @ m @ ( ord_max_real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ord_less_eq_real @ ( ord_max_real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: real] :
        ( ~ ( ( ord_less_eq_real @ ( ord_max_real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) @ X1 )
           => ~ ( genClo1015804716orrect @ m @ X1 ) )
       => sP6 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(conj_0,conjecture,
    sP6 ).

thf(h0,negated_conjecture,
    ~ sP6,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(1,plain,
    ( ~ sP5
    | ~ sP7
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP2
    | sP5
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP8
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP3
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP4
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(fact_3_tml__le__tp,axiom,
    sP7 ).

thf(fact_1_corr__m,axiom,
    sP1 ).

thf(fact_0_correct__closed,axiom,
    sP4 ).

thf(6,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,h0,fact_3_tml__le__tp,fact_1_corr__m,fact_0_correct__closed]) ).

thf(0,theorem,
    sP6,
    inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP064^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n028.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Sun Aug 27 16:52:23 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 20.57/20.79  % SZS status Theorem
% 20.57/20.79  % Mode: cade22sinegrackle2xfaf3
% 20.57/20.79  % Steps: 7039
% 20.57/20.79  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------